QG-Co2: Circumscribed Harmonic Conic


The Circumscribed Harmonic Conic is the projective transformation of the circumscribed circle of a square to the Reference Quadrigon.
See chapter QG-Tf1: QG-Projective Square Transformation.
This conic touches the sidelines of the projective circumscribed Quadrigon at the vertices of the Reference Quadrigon.
See picture below.
QG-Co2-CircumscribedHarmonicConic-01
 

Construction:
 
QG-Co2-CircumscrHarmConic-20-Constr
Equations:   
Equation QG-Co2 in 3 QA-Quadrigons in CT-notation:
  • -2 r x y  +   q x z  +   p y z = 0
  •      r x y - 2 q x z  +   p y z = 0
  •      r x y  +   q x z - 2 p y z = 0
 
Equation QG-Co2 in 3 QL-Quadrigons in CT-notation:
  •   l2 x2 + l m x y + l n x z  - m n y z = 0
  • m2 y2 + l m x y -  l n x z + m n y z = 0
  •  n2 z2 -  l m x y + l n x z + m n y z = 0
 
Equation QG-Co2 in 3 QA-Quadrigons in DT-notation:
  •      q2 r2 x- 2 p2 r2 y2 +   p2 q2 z2 = 0
  • -2 q2 r2 x2 +   p2 r2 y2 +   p2 q2 z2 = 0
  •      q2 r2 x2 +   p2 r2 y- 2 p2 q2 z2 = 0
 
Equation QG-Co2 in 3 QL-Quadrigons in DT-notation:
  •   x2 l2 - y2 m2 + z2 n2 = 0
  • -x2 l2 + y2 m2 + z2 n2 = 0
  •   x2 l2 + y2 m2 - z2 n2 = 0
 
Properties: